Work

On quaternionic bisectional curvature

Year: 2024

Type: article

Abstract: In this article we study the concept of quaternionic bisectional curvature introduced by Chow and Yang in (J Differ Geom 29(2):361–372, 1989) for quaternion-Kähler manifolds. We show that non-negative quaternionic bisectional curvature is only realized for the quaternionic projective space $$\mathbb {H}\textrm{P}^n$$ H P n . We also show that all symmetric quaternion-Kähler manifolds different from $$\mathbb {H}\textrm{P}^n$$ H P n admit quaternionic lines of negative quaternionic bisectional curvature. In particular this implies that non-negative sectional curvature does not imply non-negative quaternionic bisectional curvature. Moreover we give a new and rather short proof of a classification result by A. Gray on compact Kähler manifolds of non-negative sectional curvature.

Source: Mathematische Annalen

DOI: 10.1007/s00208-024-03028-y

Authors: Oscar Macia, Uwe Semmelmann, Gregor Weingart

Institutions: Universitat de València, University of Stuttgart, Universidad Nacional Autónoma de México

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funder: Universität Stuttgart